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arXiv:quant-ph/0401005 · Chinese Physics Letters

Information Erasure and Recovery in Quantum Memory

Cai Qing-Yu

Published Jul 1, 2004• 14 citations
arXivHTMLPDF

Abstract

We show that information in quantum memory can be erased and recovered perfectly if it is necessary. The fact that the final states of environment are completely determined by the initial states of the system allows an erasure operation to be realized by a swap operation between the system and an ancilla. Therefore, the erased information can be recovered. When there is an irreversible process, e.g. an irreversible operation or a decoherence process, in the erasure process, the information would be erased perpetually. We present that quantum erasure will also give heat dissipation in the environment. A classical limit of quantum erasure is given to coincide with Landauer's erasure principle.

DOI
10.1088/0256-307x/21/7/001

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We show that information in quantum memory can be erased and recovered perfectly if it is necessary. The fact that the final states of environment are completely determined by the initial states of the system allows an erasure operation to be realized by a swap operation between the system and an ancilla. Therefore, the erased information can be recovered. When there is an irreversible process, e.g. an irreversible operation or a decoherence process, in the erasure process, the information would be erased perpetually. We present that quantum erasure will also give heat dissipation in the environment. A classical limit of quantum erasure is given to coincide with Landauer's erasure principle.
Irreversibility has a fundamental thermodynamic cost, erasing information inevitably generates heat. This connection is quantified by the Landauer bound, which gives the minimum dissipation needed to erase a single bit of information. While this bound applies in both classical and quantum settings, it is saturated only in idealised limits of infinite resources. Here, we provide a unified first principles description of finite-resource erasure in both classical and quantum systems. We begin by proving the communal folklore that in the idealised regime the erasure cost of a bit encoded in a quantum or classical system is the same. Despite this, we show that their practical implementation differs substantially: achieving comparable erasure quality in quantum systems requires more control, larger accessible energy gaps and longer operation times. Classical protocols can achieve the erasure of a comparable quantum protocol under far weaker constraints which we expose in trade-off relations. Our results explain why practical erasure schemes fall short of Landauer's bound and show that classical systems enjoy several fundamental thermodynamic advantages.
We consider the classical algebra of observables that are diagonal in a given orthonormal basis, and define a complete decoherence process as a completely positive map that asymptotically converts any quantum observable into a diagonal one, while preserving the elements of the classical algebra. For quantum systems in dimension two and three any decoherence process can be undone by collecting classical information from the environment and using such an information to restore the initial system state. As a relevant example, we illustrate the quantum eraser of Scully et al. [Nature 351, 111 (1991)] as an example of environment-assisted correction, and present the generalization of the eraser setup for d-dimensional systems.
The Landauer principle states that any logically irreversible information processing must be accompanied by dissipation into the environment. In this Letter, we investigate the heat dissipation associated with finite-time information erasure and the effect of quantum coherence in such processes. By considering a scenario wherein information is encoded in an open quantum system whose dynamics are described by the Markovian Lindblad equation, we show that the dissipated heat is lower bounded by the conventional Landauer cost, as well as a correction term inversely proportional to the operational time. To clarify the relation between quantum coherence and dissipation, we derive a lower bound for heat dissipation in terms of quantum coherence. This bound quantitatively implies that the creation of quantum coherence in the energy eigenbasis during the erasure process inevitably leads to additional heat costs. The obtained bounds hold for arbitrary operational time and control protocol. By following an optimal control theory, we numerically present an optimal protocol and illustrate our findings by using a single-qubit system.
Erasing memory is a fundamental operational task in quantum information processing, governed by Landauer's principle, which links information loss to thermodynamic work. We introduce and analyze assisted quantum erasure, where correlations with a remote system reduce the energetic cost of resetting a memory. We identify exclusive control of erasure as the central operational requirement: only a designated party should be able to achieve the minimal cost, whereas any adversary must fail. In the device-dependent regime, we show that entanglement of formation exactly characterizes exclusivity, establishing entanglement as the decisive thermodynamic resource. Moving to a one-sided device-independent scenario, in which only the memory holder's device is trusted, we develop an operational erasure protocol based on random dephasing and conditional operations. Finally, in a fully device-independent setting, we show how Bell nonlocality and self-testing translate observed violations into lower bounds on any adversary's erasure capability, yielding a device-independent notion of exclusive thermodynamic control. Taken together, these results elevate quantum erasure from a thermodynamic constraint to an operational primitive: the erasure work cost quantifies secure, exclusive control over quantum memory, ensuring that an unauthorized agent cannot fully erase information under a bounded work budget.
Abstract. We consider the classical algebra of observables that are diagonal in a given or-thonormal basis, and define a complete decoherence process as a completely positive map that asymptotically converts any quantum observable into a diagonal one, while preserving the ele-ments of the classical algebra. For quantum systems in dimension two and three any decoherence process can be undone by collecting classical information from the environment and using such an information to restore the initial system state. As a relevant example, we illustrate the quantum eraser of Scully et al. [Nature 351, 111 (1991)] as an example of environment-assisted correction, and present the generalization of the eraser setup for d-dimensional systems. 1.
Suppose that we encode quantum information into $ n $ physical carriers. With what probabilities can we perfectly recover the quantum information after sets of carriers have been erased? This question arises in the study of quantum erasure channels, for which M.B. Hastings conjectured that if each carrier is independently erased with probability $ t \geq 1/2 $, then it is impossible to recover the quantum information with asymptotically vanishing error and probability $ > 1-t $. We prove this conjecture by establishing new no-cloning constraints on realizable recovery probabilities.